2. TEOREMA DEL PASO DE MONTAÑA
2.2. Principio Variacional de Ekeland
2.2.1. Redes
Test conditions
The tests used a reference aerofoil incidence of 5◦ with the slat and flap in their reference positions. The test used 30 m/s as the baseline velocity. However, this was too fast for the PIV system so PIV measurements for the reference configurations were obtained at the reduced velocity of 25 m/s.
The aerofoil incidence was set at 0, 5, 10, 15 and 20◦ and testing was carried out atv=10, 20 and 30 m/s. The blowing system ran with the blowing set at 0, 60, 80, 100 and 120 litres per minute (LPM). Testing ran both with and without trip strips applied to both the slat trailing edge and slat cusp.
Forces
To measure the aerodynamic forces, a 6-component balance system was used. The balance was located above the model and attached to the three struts (Figure 2.8). The wind tunnel model was large so the blockage of the wind tunnel affected the force measurements. The force measurements were corrected for wind tunnel blockage using ESDU 76 028 [144]. The forces also incorporated tare values to compensate for the impact of the struts and endplates on the force readings. The force corrections are examined in Appendix A.
Oil flow
To assess 3D features on the wing, oil flow runs were carried out at α=5◦ and 10◦. Oil flow involved applying a mixture of paraffin and titanium oxide powder to the surface of the wing. Running the wind allowed the paraffin to evaporate leaving streaks of titanium oxide, which identify the mean surface flow direction, transition and separation.
Pressure taps
The pressure taps were monitored using two ZOC systems each with 32 channels. The main element was attached to the low range zoc with a range of ±10”H2O which corresponds to maximum of CP±4.5 at 30 m/s. The slat pressure taps were
attached to the high range zoc, which had a range of ±20”H2O. Averaging the pressure over 40 seconds for each reading taken gave the mean pressure values. Recording each condition three times allowed further averaging. Repeating the runs helped in the detection of malfunctioning pressure ports, which had large differences
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between the runs. Steel tubing with an outer diameter of 1.25 mm forms the basis of the pressure taps. A 0.6 mm hole drilled in the side of the tube exposed the tube at the measurement location. The tubes were glues in the slat, to the inside of the carbon skin and sealed through the ribs that make up the pressure bulkheads between the plenum chambers. On the main element, the tubes recessed into the surface. The tubes connected to the ZOC systems using portex tubing with an inner diameter of 1 mm.
Particle image velocimetry
The PIV system used a Dantec HiSense camera and a Gemini PIV 15 laser. The laser used two tempest Ng:YAG lasers to produce twin pulses of light at up to 120mJ per pulse. The light had a wavelength of 523nm. The system was set with the laser mounted in the roof of the tunnel to illuminate the slat cove on the tunnel centre line, at the slat mid-span. The camera was fitted outside the tunnel so it could view along the slat through the glass window in the endplate (Figure 2.9). The camera was fitted with a 60 mm lens at a distance of 1,800 mm from the measurement plane while the laser was located at a distance of around 1,250 mm.
The camera synchronizes with the laser so the two images are taken when the pair of laser pulses illuminates the flow. The typical time separation between the pair of images was around 30µs. The camera had a resolution of 1,280×1,024 pixels. This represented a plot resolution of 157×125 vector maps, constructed using an area of 32×32 pixels with an overlap of 75%. Seeding particles were provided by a smoke generator located downstream of the model allowing the smoke to become more uniform as the flow passes around the closed loop tunnel. However, it was not possible to get good readings at speeds above 25 m/s. The large size of the tunnel leads to a rapid deposition of the seeding particles and the generator cannot replace them fast enough. The tunnel size also increases the attenuation of the laser sheet intensity due to the wide angle of its lens and requires increased distance between the camera and the area recorded. The slat restricting the amount of seeding entering the cove region further complicated the situation. PIV ran at 10 m/s, 20 m/s and 25 m/s. Tests at 30 m/s did not yield usable results due to inadequate seeding in the slat cove.
The PIV data gave a map of the velocity on a plane through the slat cove. Plotting the vorticity allowed the visualization of the shear layer. The vorticity is obtained from the velocity vectors using the central differencing numerical scheme used in tecplot [145]. A vorticity plot gave the direction of the flow from the cusp and showed the size and shape of the recirculation region. The vorticity plot showed
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the shear layer but was less good at picking out discrete vortices when the shear layer breaks down. Where discrete vortices are present, the Q criterion developed by Weiss and Okuba allowed their visualization [146, 147]. Subtracting the strain rate (S) from the vorticity (Ω) gave theQ value. If the value is positive, then there is a vortex. Q= 1 2(|Ω| 2− |S|2) (2.1) Ω = 1 2(∇u−(∇u) T) (2.2) S = 1 2(∇u+ (∇u) T) (2.3) Microphone readings
There were six microphones fitted around the slat (Figure 2.3) and two near the leading edge of the main element. The microphones used were Panasonic WM-60A condenser microphones, each had a diameter of 6 mm and a length of only 5 mm. The microphones were sensitive from 20 Hz to 22 kHz and gave a signal to noise ratio of 58 dB. The microphones required an operating voltage of 2V, which the pre-amps provided. The microphones on the slat were labelled S1-S6, when viewed in a clockwise direction starting from the leading edge next to the cusp. On the main element, M1 was located in the nose of the main element with M5 close to the retracted trailing edge position. Performing a fast Fourier transform (FFT) analysis on the signal from the microphones generated the frequency spectra. This FFT averaged over 100 sets of data to smooth the signal and improve the signal to noise ratio. The FFT used 2,048 samples from each data set, which was sampled at 48 kHz to give a Nyquist frequency of 23 Hz on the microphone spectra.
The surface mounted microphones had a constant response over the frequency range allowing calibration at a single point. A pistonphone allowed collection of the calibration values of the microphones; this produced a tonal signal at 1 kHz and 94 dB. To give the correct amplitude the microphone fits inside the pistonphone. For the surface microphone, this was not possible because the microphones could not detach from the wing due to the need to keep the slat pressurized. This created problems in obtaining an accurate reading of the absolute value of the sound levels, but the microphones could still monitor changes in sound level caused by alterations in the test conditions.
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Acoustic source distribution
Measuring the source distribution used a microphone array based on 56 Panasonic WM-61 microphones. The WM-61 microphones are similar to the WM-60 micro- phones except they have a reduced length of 3.4 mm and the signal to noise ratio was increased to 62 dB. After taking calibration readings, the microphone array was assembled onto a plywood panel. Cling-film covered the panel to provide a smooth cover and remove the interaction between the boundary layer and the microphone openings. The array was mounted flush with the wind tunnel ceiling 1270 mm above the model (Figure 2.10). The array recorded in 400 blocks of 512 samples at a fre- quency of 48 kHz to allow sufficient averaging. The array data gave the source strength in fourteen 1/3 octave bands from 1 kHz to 20 kHz. The array determined the SPL level over a 100×100 grid, located in the plane of the wing, to reconstruct the sound measured. The noise map was assembled using the beamforming method [148].